Word of Saint Paul from Brenton Thwaites confirms that Batman in this universe has forsaken his Thou Shall Not Kill which is horrifying enough but then one has to wonder exactly when Bruce crossed that line. Was it when Dick was still a child? Which if so brings up more disturbing inclinations about Bruce and Dicks relationship.
It seems that this particular tidbit is wrong, in 'Dick Grayson' Dick is shocked that Bruce killed the Joker, stating that Bruce has a code. Given that this is a fantasy made by Trigon to corrupt Dick, using the darkest view Dick has of Bruce, this implies that Bruce hasn't actually crossed the line, and this is either Thwaites being misinformed or a case of Lying Creator.
Dick is capable of killing Batman as we see in his All Just a Dream sequence. Furthermore, it is both a combination of his worst fear as well as deepest wish. This implies the feelings toward his mentor are outright hatred on some level rather than mere resentment.